The magnetic field inside a 5 cm diameter superconducting solenoid varies sinusoidally between 10t and 14t at a frequency of 10 hz.
a) what is the maximum electric field strength at a point 2 cm from the solenoid axis?
b) what is the value of b at the instant e reaches its maximum value?

a) E(max)= 7.5398 v/m

b) B= 2 Tesla.

Explanation:

first we need to know the  law of faraday   look the attachment to see the formula.

if r<R where R= radius of supercondunting solenoid

E(2πr) =   -d * B(πr²) / dt

E= -π/2*dB/dt

B(t)= 2+12sin(20πt)

answer for A question:

dB/dt= 12(20π) cos(20πt)

E= -r/2 (12*20π) cos(20πt)

E= -120πr cos(20πt)

max electric field strenght at:

r=2cm

r=0.02m

E(max)= (120π)*0.02)

E(max)= 7.5398 v/m

answer for question B:

value of B at the instant E reaches its maximum value

when

20πt = π, 3π, 5π,....

B= 2+12sinπ

B= 2 Tesla.

weight of the box is given as

here this is placed on the inclined of angle 42 degree

now this weight will have two components one is along the incline other is perpendicular to it

so here we need to apply a force parallel to incline opposite to its component of weight

so here the component of weight is given as

here we have

so it requires 75 n force to move it upwards

find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2